| |
Men
|
Women
|
|---|
|
Exposed cases (n)
|
100
|
200
|
|
Exposed non-cases (n)
|
400
|
300
|
|
Unexposed cases (n)
|
400
|
300
|
|
Unexposed non-cases (n)
|
100
|
200
|
|
Risk Ratio
|
0.25
|
0.6667
|
|
\(\hbox {Pr}(V=v)\)
|
0.5
|
0.5
|
|
\(\hbox {P}(Y=1 \vert A=0, V=v)\)
|
0.8
|
0.6
|
|
Weight
|
0.4
|
0.3
|
- Table shows a simple toy example of 2000 subjects, of whom 1000 are exposed to a drug. Here, the covariate V denotes gender, and we assume no unmeasured confounders. The marginal causal risk ratio can be calculated as \(\frac{0.25 \times 0.4 + 0.6667 \times 0.3}{0.4+0.3}=0.428\). Note that the weights are easy to obtain: \(\hbox {Pr}(V=v)\) is just the probability of belonging to the gender, and \(\hbox {P}(Y=1 \vert A=0, V=v)\) is the probability of the outcome among the unexposed in that gender
